Synapse is relatively RAM heavy because it leans a lot on in-memory caches to speed up DB access, as the DB schema isn't particularly intelligent and the fastest way to get it up and running was to slap caches everywhere. In the past, it could also spike RAM (which python then tends not to release back to the OS) when doing complicated merge operations of complex rooms, but this has largely been solved in the last few releases. The next generation of servers (Dendrite, Conduit, Construct) use way less RAM, having built without the time constraints (and now maintenance constraints) that impact Synapse.

Separately, it's true that Matrix intrinsically uses more resources than XMPP, because Matrix's architecture is one of replicating and persisting conversation history and state between servers, rather than passing messages. And this simply involves much more data and processing than just relaying messages between sets of users.